Suppose that a department contains 14 men and 19 women How m

Suppose that a department contains 14 men and 19 women. How many ways are there to form a committee with 6 members if it must have strictly more women than men?

Solution

For a 6 member committee , women to be more than men, the cases will be number of women as 4, 5 or 6.

Number of ways to form a 6-member committee consisting of 4 women and 2 men: 19C4 x 14C2 = 3876 X 91 = 375972

Number of ways to form a 6-member committee consisting of 5 women and 1 man: 19C5 X 14C1 = 11628 x 14 = 162792

Number of ways to form a 6-member committee consisting of 6 women and 0 men: 19C6 X 14C0 = 27132 x 1 = 27132

Number of ways to form a committee with 6 members if it must have strictly more women than men

= 375972 + 162792 + 27132 = 565896